The ability to measure time-varying fields has led to significant advances in a number of technological fields including optical chirped pulse amplification, pump-probe spectroscopy, coherent control, optical telecommunications and radar. Additionally, the temporal resolution of measurement systems is practically limited by many factors such as the bandwidth of any photodetectors used and electronics employed, consequently indirect approaches have been developed to characterize high speed electrical and optical signals.
Performing measurements in a single shot, e.g., to temporally resolve non-repetitive events, is more challenging than measuring merely repetitive signals. The equivalence between spatial diffraction and chromatic dispersion on the one hand, and the effect of a spatial lens and a quadratic temporal phase modulation on the other hand, can be used to provide temporal magnification of optical waveforms (See, e.g.,W. J. Caputi, “Stretch: a time transformation technique”, IEEE Trans. Aerosp. Electron. Syst. AES-7, 269-278 (1971); B. H. Kolner, “Space-time duality and the theory of temporal imaging”, IEEE J Quantum Electron. 30, 1951-1963 (1994)).
As is known in the art, the intensity of a signal under test can be measured in a single shot using low-speed photodetection and conventional electronics after the measured signal interacts with a chirped optical pulse for which there is a mapping between time and frequencies (See, e.g.,C. V. Bennet, E. P. Scott, and B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope”, Appl. Phys. Lett. 65 , 2515 (1994); F. G. Sun, Z. Jiang, and X.-C. Zhang, “Analysis of terahertz pulse measurement with a chirped probe beam”, Appl. Phys. Lett. 73, 2233-2235 (1998); L. Kh. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events”, IEEE J. Quantum Electron. 36, 795-801 (2000); and A. S. Bhushan, P. V. Kelkar, B. Jalai, O. Boyraz, and M. Islam, “130-GSa/s photonic analog-to-digital converter with time stretch processor”, IEEE Photon. Technol. Lett. 14, 684-686 (2002). Unfortunately however, none of these techniques provide phase information.